Numerical simulations of the effect of noise on a delayed pitchfork bifurcation

We investigate the effect of noise on a delayed pitchfork bifurcation by numerical simulations of the Langevin rate equation. When the delay is calculated averaging over a large number of trajectories that differ only on the noise realization, our results are in very good agreement with the analytical results reported in the literature (H. Zeghlache et al., Phys. Rev. A 40 (1989) 286). However, there are regions of the parameters and initial conditions for which the delay of a single trajectory is strongly influenced by noise, even for very low noise levels. Our numerical results show that in these regions the noise level at the moment when the trajectory passes the static bifurcation point might be what mainly determines the posterior evolution and delay.